Cointegration tests of PPP: do they also exhibit erratic behaviour?

Abstract

We analyse whether tests of PPP exhibit erratic behaviour (as previously reported by Caporale et al., 2003) even when (possibly unwarranted) homogeneity and proportionality restrictions are not imposed, and trivariate cointegration (stage-three) tests between the nominal exchange rate, domestic and foreign price levels are carried out (instead of stationarity tests on the real exchange rate, as in stage-two tests). We examine the US dollar real exchange rate vis-à-vis 21 other currencies over a period of more than a century, and find that stage-three test statistics are also somewhat erratic, though less than stage-two ones.

Acknowledgements

We are grateful to Alan Taylor for providing the data set used in this article, and to Walter Krämer for useful comments and suggestions.

Notes

¹ Relative PPP implies that the percentage change in the exchange rate between two currencies equals the inflation differential, i.e. .

² The two lines at the bottom are the 10 and 5% critical values calculated as in MacKinnon (1991).

Table 2.  Minimum and maximum t-test. statistics, acceptance and rejection percentages and number of available observations for each country, using CPI price series

Fig. 1. CPI-based Argentine t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

Fig. 2. CPI-based Finnish t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

Fig. 3. CPI-based Mexican t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

Fig. 4. CPI-based Chilean t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

³ Results for other countries are available upon request.

Fig. 6. GDP deflator-based Argentinean t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

Fig. 7. GDP deflator-based Danish t-stat. series using a data-dependent rule (Ng and Perron, 2001) for the choice of lags in the ADF regression

⁴ A variety of other methods could also be used to shed additional light on whether structural breaks are present (see, e.g., Ploberger and Krämer, 1996).

⁵ The results could also be interpreted as showing that as the number of observation increases, the tests become more powerful.

⁶ Again, using WPI data or a different number of lagged differences in the Johansen procedure does not make a qualitative difference. Detailed results are available upon request.

⁷ Similar patterns emerge for Australia, Brazil, Canada, Denmark, Finland, France, Mexico, the Netherlands, Norway, Portugal, Sweden and the UK, that is, 14 out of 19 countries for which the sample size is sufficiently large to make statistically meaningful statements.

⁸ More recently, panel cointegration methods have been used to deal with the issue of the low power of time series tests of PPP (see, e.g., Pedroni, 2004, and also, for an extensive survey of the literature, Caporale and Cerrato, 2006). We are currently investigating whether such methods also produce erratic behaviour.

⁹ Possible nonlinearities in exchange rates have increasingly become the focus of attention (see, e.g., Taylor, 2003.)